Among the predictions of the neolassical growth model is that countries with different levels of income per capita that are otherwise similar should experience convergence in income per capita. The figure above shows income per capita in each lower-48 US state relative to the US average for 1840, 1880, 1900, and for each year from 1929. After 1929, the coloring of the map becomes more uniform indicating gradual convergence in income per capita across the US states. This is consistent with the finding of Robert Barro and Xavier Sala-i-Martin in their 1992 paper: that there is evidence of convergence in income per capita across the US states.
The data used to produce the figure is available here:Interregional Differences in Per Capita Income, Population, and Total Income, 1840-1950 in the NBER volume Trends in the American Economy in the Nineteenth Century. Data from 1929 and after are obtained from the Bureau of Economic Analysis using a Python program available from this Github repository. The program that I used to create the map is available in the same repository. The BEA reports state-level income per capita data in current year dollars and so I convert the values to constant-year dollars using the CPI for 1840, 1880, and 1900 and the GDP deflator for 1929 and after.
The data on this site are updated as new data becomes available. Please send feedback to me at firstname.lastname@example.org.